Violation in Mixing

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188 Analysis of the time-dependent �È -violating asymmetry in � � � � decays The kinematics of two-body decay are taken into account in the toy Monte Carlo generator: ¯ generate a � meson in the § �Ë frame with momentum randomly selected from a Gaussian distribution (� � Å�Î� , � � Å�Î� ) and polar angle selected from a Ó× � distribution, ¯ decay the � candidate to two tracks isotropically, ¯ boost to the laboratory frame, ¯ use the resulting track momenta and polar angles to compute the expected value of � and ¡�. This “generation” procedure faithfully reproduces the (� �� ) and ¡�� correlations observed in Table 7-14. In the case the data ¡� resolution ( � Å�Î) is used instead of the Monte Carlo value ( � Å�Î) the correlation between ¡� and � is reduced. 7.8.2 Effect of floating yields in the �È fit The rms of the ¡Ø distribution for �� events is greater than the corresponding rms for continuum ÕÕ events. It is therefore expected that adding this variable in the likelihood function will improve the statistical separation between signal and background. To see how much we gain in the branching fraction analysis by floating yields in the �È fit, we generated 685 toy experiments and fit each one with and without the ¡Ø PDF in the likelihood. Figure 7-14 shows the difference in the fitted error on Æ�� and the two asymmetry parameters. The error on Æ�� improves by � , while the asymmetry errors increase only slightly. The conclusion is that fitting simultaneously for yields and asymmetries optimizes the branching fraction measurement and leads to a more accurate asymmetry measurement (since the uncertainty on the yield is included directly in the fit error). 7.8.3 Monte Carlo fits Since we expect � � signal �� and Ã� events in fb , an important consistency check on the ¡Ø resolution function, and in the fit mechanism itself, is to fit for the � lifetime and mixing frequency in the � � sample. Table 7-15 shows the results of several test fits on Monte Carlo samples. Fitting for the lifetime and ¡Ñ�� in pure signal, or in a mix of �� and Ã� events in the proper ratio, returns correct values for both parameters. We have also tried mixing the correct signal yield into the �� fb continuum Monte Carlo sample and find consistent values of � and ¡Ñ�� . Finally, fitting for Ë�� and �� returns the correct values in high statistics signal Monte Carlo and consistent values in the sample with background. To check that the fit errors on the �È asymmetries in simulated Monte Carlo samples are consistent with what we estimate in toy Monte Carlo, we take the same sample of �� fb continuum Monte Carlo and add in ten different sets of (Æ��,ÆÃ�) with exact values determined by Poisson statistics. Table 7-16 summarizes the results of this test. The average error on Ë�� and �� are � and ��, respectively. Scaled to fb we would predict an expected error of �� on Ë�� and ��, in excellent agreement with the toy Monte Carlo prediction (Fig. 7-12). MARCELLA BONA
7.8 Validation studies 189 Figure 7-14. Difference in the fit error on Æ �� (left) and the two �È parameters (right) with and without floating yields in the �È fit. The average error on Æ �� is � , so the improvement in statistical error is � . Sample � Ô× ¡Ñ�� Ô× Ë�� ¦ � fixed fixed fixed � �� fixed fixed � �� ¦ � � � ¦ � � � � Ã� fixed �� ¦ � fixed fixed � � Ã� �� ¦ � fixed fixed fixed � � �� + � � Ã� �� ¦ � � fixed fixed fixed � � �� + � � Ã� fixed fixed � �� ¦ � �� ¦ � �� fb equiv. �� ¦ � fixed fixed fixed �� fb equiv. fixed fixed �� ¦ �� ¦ �� fb equiv. fixed �� ¦ � �� fixed fixed �� fb equiv. fixed �� ¦ � �� ¦ �� ¦ �� Table 7-15. Lifetime, ¡Ñ��, and �È fits to various signal and background Monte Carlo samples. The generated values are: � � �� Ô×, ¡Ñ�� Ô× , Ë�� , and �� . When fixed, the fit parameters are set to: � � �� Ô×, ¡Ñ�� Ô× , Ë�� . ANALYSIS OF THE TIME-DEPENDENT �È -VIOLATING ASYMMETRY IN � � � � DECAYS
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ÍÒ�Ú�Ö×�Ø��
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Contents Introduction . ...........
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4 Strategy and Tools for Charmless
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7.2 Branching fraction � � �
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Introduction The main goal of the B
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1 �È Violation in the �� Sys
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1.2 Neutral � Mesons 7 Note, howe
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1.2 Neutral � Mesons 9 Applying t
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1.2 Neutral � Mesons 11 �È �
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1.2 Neutral � Mesons 13 ��
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1.2 Neutral � Mesons 15 � ¡�
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1.2 Neutral � Mesons 17 and � a
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1.2 Neutral � Mesons 19 given tim
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1.3 The Three Types of �È Violat
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1.4 �È Violation in the Standard
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1.5 Determination of « 37 1.5 Dete
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1.5 Determination of « 39 Assuming
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1.5 Determination of « 41 Figure 1
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1.5 Determination of « 43 b q (a)
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1.5 Determination of « 45 � �
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2 The BABAR Experiment 2.1 Physics
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2.1 Physics at � � B Factory op
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2.2 The BABAR detector. 51 Integrat
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2.2 The BABAR detector. 53 The dete
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2.2 The BABAR detector. 55 two oute
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2.2 The BABAR detector. 57 SVT Effi
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2.2 The BABAR detector. 59 324 1015
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Efficiency 2.2 The BABAR detector.
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2.2 The BABAR detector. 63 2.2.4 Th
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entries per mrad 2.2 The BABAR dete
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2.2 The BABAR detector. 67 entries
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2.2 The BABAR detector. 69 energies
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2.2 The BABAR detector. 71 The main
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Efficiency 2.2 The BABAR detector.
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2.2 The BABAR detector. 75 Table 2-
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3 Ã Ë reconstruction and efficien
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3.3 Studies on data 79 19.5° BINS
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3.3 Studies on data 81 ¯ off-reson
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3.3 Studies on data 83 0.504 0.502
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3.3 Studies on data 85 0.03 0.025 0
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3.3 Studies on data 87 0.504 0.502
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3.3 Studies on data 89 N(π + π -
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3.3 Studies on data 91 0.508 0.506
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3.3 Studies on data 93 Figure 3-13.
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3.3 Studies on data 95 0.508 0.506
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4 Strategy and Tools for Charmless
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4.2 Event selection 99 channel sele
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4.2 Event selection 101 ÀÐ �
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4.2 Event selection 103 Figure 4-2.
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4.3 Background fighting 105 Figure
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4.4 PID selection 107 In the case o
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4.4 PID selection 109 θ c Cut Effi
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4.5 Tracking Corrections 111 Ë�
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4.6 Analysis methods 113 Ñ�Ë si
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4.6 Analysis methods 115 Events/2.5
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4.6 Analysis methods 117 Figure 4-1
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4.6 Analysis methods 119 θ c radia
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5 Measurement of Branching Fraction
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5.2 Ã Ë reconstruction 123 1 0.8
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5.3 Analysis Strategy 125 0.35 0.3
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5.4 Background Suppression and PDF
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5.5 Maximum likelihood analysis 133
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5.5 Maximum likelihood analysis 135
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Page 151 and 152: 5.6 Counting analysis 145 Table 5-1
Page 153 and 154: 5.7 Determination of branching frac
Page 155 and 156: 6 Measurement of Branching Fraction
Page 157 and 158: 6.3 The maximum likelihood analysis
Page 163 and 164: 6.4 Counting analysis 157 120 100 8
Page 165 and 166: 6.5 Analysis choice 159 6.5 Analysi
Page 167 and 168: 6.6 Results on the Run1 data-set 16
Page 169 and 170: 6.7 Determination of the branching
Page 171 and 172: 7 Analysis of the time-dependent
Page 173 and 174: 7.3 Analysis strategy 167 Parameter
Page 175 and 176: 7.4 Data samples and event selectio
Page 177 and 178: 7.4 Data samples and event selectio
Page 179 and 180: 7.5 Background characterization 173
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Page 191 and 192: 7.8 Validation studies 185 Figure 7
Page 193: 7.8 Validation studies 187 100 75 5
Page 197 and 198: 7.8 Validation studies 191 Paramete
Page 199 and 200: 7.9 Results 193 Parameter Fit Resul
Page 201 and 202: 7.9 Results 195 Events/2 MeV/c 2 Ev
Page 203 and 204: 7.10 Systematic studies 197 Categor
Page 205 and 206: 7.11 Summary 199 �Ã� Ë��
Page 207 and 208: 7.11 Summary 201 �Ã� Ë��
Page 209 and 210: 7.11 Summary 203 Variation �Ã�
Page 211 and 212: BIBLIOGRAFIA 205 Bibliografia Chapt
Page 213 and 214: BIBLIOGRAFIA 207 [38] J. Charles, P
Page 215 and 216: BIBLIOGRAFIA 209 Chapter 7 [67] D.
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Violation in Mixing

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